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Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral. See attachment

Mathematics
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I tried to do this and have got so far that AB = AC
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Other answers:

I took following triangles :ABF and AEC by AAS I got both of these triangles congruent and therefore by CPCT AB = AC
(CPCT = Congruent Parts of Congruent Triangles are equal)
That idea should work to get that AB=BC as well.
So far , we have got ABC as isosceles. Now, I took triangle ABC and AFC both of these triangles are congruent by RHS BF = FC ( by CPCT ) therefore F is mid point of BC an AF is median and altitude also Therefore , this is the property of an equilateral triangle , so ABC is an equi. triangle
Is this correct?
You mean to take ABE and BEC triangles @joemath314159 ?
yep. and do exactly what you did with the other triangles again.
I meant this : ADC and ABD in the above comment.
OK wait..
I think I had tried that earlier but I didnt' get any favorable result , wait let me do it again
there are many combinations you could take. The pair I see is triangles BEC and BDA.
Oh yes that will work ... BEC and BDA .. this gives some output to me.
Thanks a lot @joemath314159 for your help .. Might gonna work in more concentration for me..

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